Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128408 | C2 | semidirect |
| 3. #19128052 | C2 | semidirect |
| 4. #19128032 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127959 | C2 | semidirect |
| 7. #19127912 | C2 | semidirect |
| 8. #19127865 | C2 | semidirect |
| 9. C4×#13050579 | C2 | semidirect |
| 10. #19127703 | C2 | semidirect |
| 11. #436×C83 | C2 | semidirect |
| 127. C83 | #3331 | semidirect |
| 137. #436 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128408 | 2 |
| #19128356 | 2 |
| #19128052 | 2 |
| #19128032 | 2 |
| #19127992 | 2 |
| #19127959 | 2 |
| #19127912 | 2 |
| #19127865 | 2 |
| C4×#13050579 | 2 |
| #19127703 | 2 |
| #436×C83 | 2 |
| #3331 | 83 |